Multivariable feedback, sensitivity, and decentralized control

In this paper the problem of sensitivity, reduction by feedback is studied and related to a problem of decentralized control. A plant will be represented by an
N \times N
matrix of frequency responses, which may be unstable or irrational. The object will be to find conditions on
P(s)
under which a diagonal feedback
F(s)
can make the sensitivity
\parallel{I + P(s)F(s)}^{-1}\parallel
arbitrarily small over some specified frequency interval [
-j\omega_{0}, j\omega_{0}
] without violating a global sensitivity, bound
\parallel{I+ P(s)F(s)}^{-1}\parallel \leq M
, (
M\geq
some const. >1) for
Re(s) \geq 0
. It will be shown that such a diagonal feedback of the "high gain" type can be constructed whenever
P^{-1}(s)
is analytic in
Re(s)\geq 0, P(s)
satisfies an attenuation condition near
s = \infty
, and
P(s)
approaches diagonal dominance at high frequencies. It will also be shown that these conditions on the plant can be interpreted as conditions for the existence of a decentralized wide-band control scheme.